Quantum Computing cracking Bitcoin

# The Quantum Computing Threat: A Formal Economic Analysis of Its Potential to Ruin Bitcoin

## 1. Introduction

Bitcoin, launched in 2009, has positioned itself as a secure, decentralized digital asset reliant on cryptographic protocols for its integrity. However, advancements in quantum computing pose a profound existential risk to these foundations. This essay develops a formal argument that quantum computing could effectively ruin Bitcoin by undermining its security model, leading to a collapse in trust, value, and viability. Under rational market assumptions, we assume that investors prioritize security and that technological disruptions can erode asset fundamentals irreversibly. The analysis is structured with clear definitions, derivations, and evidence from recent developments as of February 2026, avoiding polemic while maintaining argumentative stringency for publication as a discussion paper.

## 2. Definition of Key Concepts

### 2.1 Quantum Computing and Cryptographic Vulnerabilities

Quantum computing leverages quantum bits (qubits) to perform computations exponentially faster than classical computers for specific problems. Relevant algorithms include:

- Shor's Algorithm: Factors large integers and solves discrete logarithm problems in polynomial time, breaking asymmetric cryptography like Elliptic Curve Digital Signature Algorithm (ECDSA), which Bitcoin uses for transaction signatures.

- Grover's Algorithm: Provides a quadratic speedup for searching unsorted databases, potentially weakening hash functions like SHA-256 used in Bitcoin's proof-of-work.

Bitcoin's security model assumes the computational infeasibility of reversing public keys to private keys. A cryptographically relevant quantum computer (CRQC) would violate this assumption, exposing funds.

### 2.2 Ruin in Economic Terms

"Ruin" for Bitcoin is defined as a state where:

1. Security breaches enable widespread theft or forgery.

2. Market confidence erodes, leading to a price collapse.

3. Network participation declines due to perceived fragility.

Formally, Bitcoin's value \( V_{BTC} \) depends on trust \( T \):

\[

V_{BTC} = f(T, S, D)

\]

Where \( S \) is scarcity and \( D \) is demand. If quantum advances reduce \( T \to 0 \), then \( V_{BTC} \to 0 \).

## 3. How Quantum Computing Breaks Bitcoin's Cryptography

Bitcoin's protocol relies on ECDSA for ownership verification and SHA-256 for mining and address hashing. Shor's Algorithm could derive private keys from public keys in minutes, a task requiring billions of years on classical hardware. As of 2026, estimates suggest 20–50% of Bitcoin addresses (holding 4.5–6.7 million BTC, valued at $500–600 billion) are vulnerable due to exposed or reused public keys.

Grover's Algorithm could halve the effective security of SHA-256, making 51% attacks or preimage attacks feasible with sufficient qubits. Recent projections indicate a 19–34% probability of public-key encryption breakage by 2034, rising to 60–82% by 2044. Institutions like Jefferies have already removed Bitcoin from portfolios citing these risks, signaling early market recognition.

## 4. Economic Impacts on Bitcoin's Network and Value

A quantum breach would trigger immediate economic fallout:

- Theft and Loss: Exposed addresses could be drained, leading to a supply shock and panic selling. Formally, if a fraction \( \alpha \) of supply (e.g., 25%) is stolen, market capitalization drops by \( \alpha \times P_{BTC} \), amplifying volatility.

- Erosion of Trust: As a store of value, Bitcoin's utility hinges on immutability. Quantum threats could shift expected utility for risk-averse holders:

\[

E(U) = E(R) - \frac{1}{2} \lambda (\sigma^2 + Q_r)

\]

Where \( Q_r \) is quantum risk premium, potentially rendering \( E(U) < 0 \).

- Network Fragility: Miners might exit if security perceptions falter, reducing hashrate \( H \):

\[

H = g(P_{BTC}, T)

\]

A feedback loop ensues: lower \( H \) increases vulnerability, further depressing \( P_{BTC} \).

Recent actions, such as Coinbase forming a quantum advisory board, underscore the reality of this threat.

## 5. Challenges in Mitigating the Threat

Proponents argue Bitcoin can upgrade to post-quantum cryptography (PQC) via soft forks, such as Bitcoin Improvement Proposal 360 or hash-based signatures. However, challenges abound:

- Migration Complexity: Transitioning requires consensus, potentially forking the chain and exposing legacy addresses during the process.

- Timeline Mismatch: Quantum advances may outpace upgrades. Experts like Nic Carter warn developers are underestimating the threat, with practical CRQCs possibly arriving in 2–9 years.

- Harvest-Now-Decrypt-Later (HNDL): Adversaries are already archiving encrypted data for future decryption, amplifying retrospective risks.

On platforms like X, discussions highlight quantum as a "long-term risk, not immediate," but initiatives like MicroStrategy's Bitcoin Security Program indicate growing concern.

## 6. Broader Systemic Risks

Beyond Bitcoin, quantum threats extend to financial systems, but Bitcoin's decentralized nature lacks centralized authority for swift upgrades, unlike banks. This could lead to a "quantum-exposed" equilibrium where only quantum-resistant assets survive, marginalizing Bitcoin.

Formally, in a Greater Fool model augmented by quantum risk:

\[

P_{BTC} = E(P_{t+1}) - Q_c

\]

Where \( Q_c \) is the cost of quantum compromise, driving \( P_{BTC} \to 0 \) upon realization.

## 7. Why the Ruin is Plausible Despite Current Stability

As of February 2026, Bitcoin trades around $65,000, but quantum risks are influencing decisions, as seen in portfolio rebalances and advisory formations. These are transient stabilizers; a breakthrough could accelerate collapse.

## 8. Conclusion

Quantum computing threatens to ruin Bitcoin by breaking its cryptographic pillars, eroding trust, and triggering economic cascades. With vulnerable addresses, migration hurdles, and advancing timelines, the risk is substantive. Formally:

\[

\boxed{V_{BTC}^{post-quantum} \to 0}

\]

Bitcoin's survival demands proactive PQC adoption, but delays could prove fatal, transforming it from a digital gold to a relic of pre-quantum security.